In the interfacial superconductor Bi2Te3/Fe1+yTe, two dimensional superconductivity occurs in direct vicinity to the surface state of a topological insulator. If this state were to become involved in superconductivity, under certain conditions a topological superconducting state could be formed, which is of high interest due to the possibility of creating Majorana fermionic states. We report directional point-contact spectroscopy data on the novel Bi2Te3/Fe1+yTe interfacial superconductor for a Bi2Te3 thickness of 9 quintuple layers, bonded by van der Waals epitaxy to a Fe1+yTe film at an atomically sharp interface. Our data show highly unconventional superconductivity, which appears as complex as in the cuprate high temperature superconductors. A very large superconducting twin-gap structure is replaced by a pseudogap above ~12 K which persists up to 40 K. While the larger gap shows unconventional order parameter symmetry and is attributed to a thin FeTe layer in proximity to the interface, the smaller gap is associated with superconductivity induced via the proximity effect in the topological insulator Bi2Te3.